Density Matrix Renormalization Group Technique Research Articles

Mott-superfluid transition for spin-orbit-coupled bosons in one-dimensional optical lattices

We study the effects of spin-orbit coupling on the Mott-superfluid transition of bosons in a one-dimensional optical lattice. We determine the strong-coupling magnetic phase diagram by a combination of exact analytic and numerical means. Smooth evolution of the magnetic structure into the superfluid phases is investigated with the density matrix renormalization group technique. Other magnetic phases are seen and phase transitions between them within the superfluid regime are discussed. Possible experimental detection is discussed.

Low-lying excited states in armchair polyacene within Pariser-Parr-Pople model: A density matrix renormalization group study

We studied the nature of the ground state and low-lying excited states of armchair polyacene oligomers (Polyphenanthrene) within long-range Pariser-Parr-Pople model Hamiltonian with up to 14 monomers using symmetrized density matrix renormalization group technique. The ground state of all armchair polyacenes studied is found to be singlet. The results show that lowest singlet dipole allowed excited state has higher energy for armchair polyacenes as compared to linear fused polyacenes. Moreover, unlike linear fused polyacenes, the lowest singlet excited state of these oligomers is always found to lie below the lowest dipole forbidden two-photon state indicating that these armchair polyacene oligomers strongly fluoresce. The calculations of low-lying excitations on singly and triply electron doped armchair polyacene oligomers show a low energy band with strong transition dipole moment that coupled to charge conductivity. This implies armchair polyacene posses novel field-effect transistor properties.

From fractionally charged solitons to Majorana bound states in a one-dimensional interacting model

We consider one-dimensional topological insulators hosting fractionally charged midgap states in the presence and absence of induced superconductivity pairing. Under the protection of a discrete symmetry, relating positive and negative energy states, the solitonic midgap states remain pinned at zero energy when superconducting correlations are induced by proximity effect. When the superconducting pairing dominates the initial insulating gap, Majorana fermion phases develop for a class of insulators. As a concrete example, we study the Creutz model with induced $s$-wave superconductivity and repulsive Hubbard-type interactions. For a finite wire, without interactions, the solitonic modes originating from the nonsuperconducting model survive at zero energy, revealing a fourfold-degenerate ground state. However, interactions break the aforementioned discrete symmetry and completely remove this degeneracy, thereby producing a unique ground state which is characterized by a topological bulk invariant with respect to the product of fermion parity and bond inversion. In contrast, the Majorana edge modes are globally robust to interactions. Moreover, the parameter range for which a topological Majorana phase is stabilized expands when increasing the repulsive Hubbard interaction. The topological phase diagram of the interacting model is obtained using a combination of mean-field theory and density matrix renormalization group techniques.

Geometry-induced pair condensation

We study a one-dimensional model of interacting bosons on a lattice with two flat bands. Regular condensation is suppressed due to the absence of a well defined minimum in the single particle spectrum. We find that interactions stabilize a number of non-trivial phases like a pair (quasi-) condensate, a supersolid at incommensurable fillings and valence bond crystals at commensurability. We support our analytical calculations with numerical simulations using the density matrix renormalization group technique. Implications for cold-atoms and extensions to higher dimensions are discussed.

One-dimensional Bose-Hubbard model with local three-body interactions

We employ the (dynamical) density-matrix renormalization-group technique to investigate the ground-state properties of the Bose-Hubbard model with nearest-neighbor transfer amplitudes $t$ and local two-body and three-body repulsion of strength $U$ and $W$, respectively. We determine the phase boundaries between the Mott-insulating and superfluid phases for the lowest two Mott lobes from the chemical potentials. We calculate the tips of the Mott lobes from the Tomonaga-Luttinger liquid parameter and confirm the positions of the Kosterlitz-Thouless points from the von Neumann entanglement entropy. We find that physical quantities in the second Mott lobe such as the gap and the dynamical structure factor scale almost perfectly in $t/(U+W)$, even close to the Mott transition. Strong-coupling perturbation theory shows that there is no true scaling but deviations from it are quantitatively small in the strong-coupling limit. This observation should remain true in higher dimensions and for not too large attractive three-body interactions.

Critical Casimir forces along the isofields

Using quasiexact numerical density-matrix renormalization-group techniques we calculate the critical Casimir force for a two-dimensional (2D) Ising strip with equal strong surface fields, along the thermodynamic paths corresponding to the fixed nonzero bulk field h≠0. Using the Derjaguin approximation we also determine the critical Casimir force and its potential for two disks. We find that varying the temperature along the isofields lying between the bulk coexistence and the capillary condensation critical point leads to a dramatic increase of the critical Casimir interactions with a qualitatively different functional dependence on the temperature than along h=0. These findings might be of relevance for biomembranes, whose heterogeneity is recently interpreted as being connected with a critical behavior belonging to the 2D Ising universality class.

Restoring phase coherence in a one-dimensional superconductor using power-law electron hopping

In a one-dimensional (1D) superconductor, zero temperature quantum fluctuations destroy phase coherence. Here we put forward a mechanism which can restore phase coherence: power-law hopping. We study a 1D attractive-U Hubbard model with power-law hopping by Abelian bosonization and density-matrix renormalization group (DMRG) techniques. The parameter that controls the hopping decay acts as the effective, non-integer spatial dimensionality $d_{eff}$. For real-valued hopping amplitudes we identify analytically a range of parameters for which power-law hopping suppress fluctuations and restore superconducting long-range order for any $d_{eff} > 1$. A detailed DMRG analysis fully supports these findings. These results are also of direct relevance to quantum magnetism as our model can be mapped onto a S=1/2 XXZ spin-chain with power-law decaying couplings, which can be studied experimentally by cold ion-trap techniques.

Adiabatic Tracking of a State: A New Route to Nonequilibrium Physics

We present a novel numerical approach to track the response of a quantum system to an external perturbation that is progressively switched on. The method is applied, within the framework of the density matrix renormalization group technique, to track current-carrying states of interacting fermions in one dimension and in the presence of an Aharonov-Bohm magnetic flux. This protocol allows us to access highly excited states. We also discuss the connection with the entanglement entropy of these excited states.

Linear and Nonlinear Optical Properties of Expanded Porphyrins: A DMRG Study

We study absorption spectra and two photon absorption coefficient of expanded porphyrins (EPs) by the density matrix renormalization group (DMRG) technique. We employ the Pariser-Parr-Pople (PPP) Hamiltonian which includes long-range electron-electron interactions. We find that, in the 4n+2 EPs, there are two prominent low-lying one-photon excitations, while in 4n EPs, there is only one such excitation. We also find that 4n+2 EPs have large two-photon absorption cross sections compared to 4n EPs. The charge density rearrangement in the one-photon excited state is mostly at the pyrrole nitrogen site and at the meso carbon sites. In the two-photon states, the charge density rearrangement occurs mostly at the aza-ring sites. In the one-photon state, the C-C bond length in aza rings shows a tendency to become uniform. In the two-photon state, the bond distortions are on C-N bonds of the pyrrole ring and the adjoining C-C bonds which connect the pyrrole ring to the aza or meso carbon sites.

Double zigzag spin chain in a strong magnetic field close to saturation

We study the ground state phase diagram of a frustrated spin tube in a strong external magnetic field. This model can be viewed as two coupled zigzag spin chains, or as a two-leg spin ladder with frustrating next-nearest-neighbor couplings along the legs, and its study is motivated by the physics of such materials as Sulfolane-Cu_{2}Cl_{4} and BiCu_{2}PO_{6}. In magnetic fields right below the saturation, the system can be effectively represented as a dilute gas of two species of bosonic quasiparticles that correspond to magnons with inequivalent incommensurate momenta at two degenerate minima of the magnon dispersion. Using the method previously proposed and tested for frustrated spin chains, we calculate effective interactions in this two-component Bose gas. On this basis, we establish the phase diagram of nearly-saturated frustrated spin tube, which is shown to include the two-component Luttinger liquid, two types of vector chiral phases, and phases whose physics is determined by the presence of bound magnons. We study the phase diagram of the model numerically by means of the density matrix renormalization group technique, and find a good agreement with our analytical predictions.

Spin polarization in the Hubbard model with Rashba spin-orbit coupling on a ladder

The competition between on-site Coulomb repulsion and Rashba spin-orbit coupling (RSOC) is studied on two-leg ladders by numerical techniques. By studying persistent currents in closed rings by exact diagonalization, it is found that the contribution to the current due to the RSOC V_{SO}, for a fixed value of the Hubbard repulsion U reaches a maximum at intermediate values of V_{SO}. By increasing the repulsive Hubbard coupling U, this spin-flipping current is suppressed and eventually it becomes opposite to the spin-conserving current. The main result is that the spin accumulation defined as the relative spin polarization between the two legs of the ladder is enhanced by U. Similar results for this Hubbard-Rashba model are observed for a completely different setup in which two halves of the ladders are connected to a voltage bias and the ensuing time-dependent regime is studied by the density matrix-renormalization group technique. It is also interesting a combined effect between V_{SO} and U leading to a strong enhancement of antiferromagnetic order which in turn may explain the observed behavior of the spin-flipping current. The implications of this enhancement of the spin-Hall effect with electron correlations for spintronic devices is discussed.

Heisenberg antiferromagnet on Cayley trees: Low-energy spectrum and even/odd site imbalance

To understand the role of local sublattice imbalance in low-energy spectra of s=1/2 quantum antiferromagnets, we study the s=1/2 quantum nearest neighbor Heisenberg antiferromagnet on the coordination 3 Cayley tree. We perform many-body calculations using an implementation of the density matrix renormalization group (DMRG) technique for generic tree graphs. We discover that the bond-centered Cayley tree has a quasidegenerate set of a low-lying tower of states and an "anomalous" singlet-triplet finite-size gap scaling. For understanding the construction of the first excited state from the many-body ground state, we consider a wave function ansatz given by the single-mode approximation, which yields a high overlap with the DMRG wave function. Observing the ground-state entanglement spectrum leads us to a picture of the low-energy degrees of freedom being "giant spins" arising out of sublattice imbalance, which helps us analytically understand the scaling of the finite-size spin gap. The Schwinger-boson mean-field theory has been generalized to nonuniform lattices, and ground states have been found which are spatially inhomogeneous in the mean-field parameters.

Magnetic states of the two-leg-ladder alkali metal iron selenidesAFe2Se3

Recent neutron scattering experiments addressing the magnetic state of the two-leg-ladder selenide compound BaFe${}_{2}$Se${}_{3}$ have unveiled a dominant spin arrangement involving ferromagnetically ordered 2$\phantom{\rule{0.16em}{0ex}}\ifmmode\times\else\texttimes\fi{}\phantom{\rule{0.16em}{0ex}}$2 iron superblocks, that are antiferromagnetically coupled among them (the ``block-AFM''state). Using the electronic five-orbital Hubbard model first-principles techniques to calculate the electronic hopping amplitudes between irons, and the real-space Hartree-Fock approximation to handle the many-body effects, here it is shown that the exotic block-AFM state is indeed stable at realistic electronic densities close to $n\ensuremath{\sim}6.0$. Another state with parallel spins along the rungs and antiparallel along the legs of the ladders (the ``CX'' state) is close in energy. This state becomes stable in other portions of the phase diagrams, such as with hole doping, as also found experimentally via neutron scattering applied to KFe${}_{2}$Se${}_{3}$. In addition, the present study unveils other competing magnetic phases that could be experimentally stabilized by varying either $n$ chemically or the electronic bandwidth by pressure. Similar results were obtained using two-orbital models, studied here via Lanczos and density-matrix renormalization group (DMRG) techniques. A comparison of the results obtained with the realistic selenides hopping amplitudes for BaFe${}_{2}$Se${}_{3}$ against those found using the hopping amplitudes for pnictides reveals several qualitative similarities, particularly at intermediate and large Hubbard couplings.

Discrete antiferromagnetic spin-wave excitations in the giant ferric wheel Fe18

The low-temperature elementary spin excitations in the AFM molecular wheel Fe18 were studied experimentally by inelastic neutron scattering and theoretically by modern numerical methods, such as dynamical density matrix renormalization group or quantum Monte Carlo techniques, and analytical spin-wave theory calculations. Fe18 involves eighteen spin-5/2 Fe(III) ions with a Hilbert space dimension of 10^14, constituting a physical system that is situated in a region between microscopic and macroscopic. The combined experimental and theoretical approach allowed us to characterize and discuss the magnetic properties of Fe18 in great detail. It is demonstrated that physical concepts such as the rotational-band or L&E-band concepts developed for smaller rings are still applicable. In particular, the higher-lying low-temperature elementary spin excitations in Fe18 or AFM wheels in general are of discrete antiferromagnetic spin-wave character.

Quantum phase diagram of the frustrated spin ladder with next-nearest-neighbor interactions

Using the density matrix renormalization group technique, we investigate the quantum phase diagram of a ferromagnetic frustrated two-leg spin-1/2 ladder with diagonal and in-chain next-nearest-neighbor (NNN) interactions. By analyzing the correlation function and four-site entropy, we obtain the quantum phase diagram of the system. We find that the system possesses a tetramer phase, a ferromagnetic phase and states I and II. Spin arrangements for states I and II are also determined. In addition, the influence of the in-chain NNN interaction J2 on the phase transitions of the anti-ferromagnetic case is studied. We show the phase diagram and find that the stagger dimer phase exists only in a narrow parameter region. Meanwhile, the existence of the controversial columnar dimer phase at J2 = 0 is carefully analyzed.

Phase diagram of the extended Bose–Hubbard model

By means of the density matrix renormalization group technique, we accurately determine the zero-temperature phase diagram of the one-dimensional extended Bose–Hubbard model with on-site and nearest-neighbor interactions. We analyze the scaling of the charge and of the neutral ground-state energy gaps, as well as of various order parameters. In this way we come to an accurate location of the boundaries between the superfluid and the insulating phases. In this last region, we are able to distinguish between the conventional Mott insulating and density-wave phases and the Haldane insulator phase displaying long-range string ordering, as originally predicted by Dalla Torre et al (2006 Phys. Rev. Lett.97 260401).

Slow quench dynamics of Mott-insulating regions in a trapped Bose gas

We investigate the dynamics of Mott-insulating regions of a trapped bosonic gas as the interaction strength is changed linearly with time. The bosonic gas considered is loaded into an optical lattice and confined to a parabolic trapping potential. Two situations are addressed: the formation of Mott domains in a superfluid gas as the interaction is increased, and their melting as the interaction strength is lowered. In the first case, depending on the local filling, Mott-insulating barriers can develop and hinder the density and energy transport throughout the system. In the second case, the density and local energy adjust rapidly whereas long range correlations require longer time to settle. For both cases, we consider the time evolution of various observables: the local density and energy, and their respective currents, the local compressibility, the local excess energy, the heat and single particle correlators. The evolution of these observables is obtained using the time-dependent density-matrix renormalization group technique and comparisons with time-evolutions done within the Gutzwiller approximation are provided.

Discrete symmetry breaking transitions between paired superfluids

We explore the zero-temperature phase diagram of bosons interacting via Feshbach resonant pairing interactions in one dimension. Using DMRG (Density Matrix Renormalization Group) and field theory techniques we characterize the phases and quantum phase transitions in this low-dimensional setting. We provide a broad range of evidence in support of an Ising quantum phase transition separating distinct paired superfluids, including results for the energy gaps, correlation functions and entanglement entropy. In particular, we show that the Ising correlation length, order parameter and critical properties are directly accessible from a ratio of the atomic and molecular two-point functions. We further demonstrate that both the zero-momentum occupation numbers and the visibility are in accordance with the absence of a purely atomic superfluid phase. We comment on the connection to recent studies of boson pairing in a generalized classical XY model.

Testing the universality of the many-body metal-insulator transition by time evolution of a disordered one-dimensional ultracold fermionic gas

It is now possible to study experimentally the combined effect of disorder and interactions in cold atom physics. Motivated by these developments we investigate the dynamics around the metal-insulator transition (MIT) in a one-dimensional (1D) Fermi gas with short-range interactions in a quasiperiodic potential by the time-dependent density-matrix renormalization group (tDMRG) technique. By tuning disorder and interactions we study the MIT from the weakly to the strongly interacting limit. The MIT is not universal as time evolution, well described by a process of anomalous diffusion, depends qualitatively on the interaction strength. By using scaling ideas we relate the parameter that controls the diffusion process with the critical exponent that describes the divergence of the localization length. In the limit of strong interactions theoretical arguments suggest that the motion at the MIT tends to ballistic and critical exponents approach mean-field predictions.

Ground-state properties of antiferromagnetic anisotropicS=1Heisenberg spin chains

Using (infinite) density-matrix renormalization-group techniques, ground-state properties of antiferromagnetic $S=1$ Heisenberg spin chains with exchange and single-site anisotropies in an external field are studied. The phase diagram is known to display a plenitude of interesting phases. We elucidate quantum phase transitions between the supersolid and spin-liquid phases as well as the spin-liquid and ferromagnetic phases. Analyzing spin-correlation functions in the spin-liquid phase, commensurate and (two distinct) incommensurate regions are identified.